Exporting interactive Flash content
It is possible to export a raster animation for Flash, (.flv). There are no Blender plugins (or native features) that let you author .fla or .swf interactive content. Some parts of the flash format remain closed source, but if someone really wanted they could using the MXMLC compiler. 

The grasp that Flash once had on the interactive web has faded significantly with the growing improvements in JavaScript and adjacent technologies. Egged on a little by Apple's decision to stop supporting Flash directly on it's mobile devices. In light of recent (July 2015) revelations about years-old, but profound, security issues, the public's sense of trust in Flash isn't improving.

There are solutions for getting Blender content online and animated + interactive: 


Code WebGL directly
Three.js
Blend4Web 


intended to make the process a lot easier, a shining endorsement is the fact that NASA uses it. See this other answer about interactive web tech built with a direct pipeline from Blender.
Why the blender browser plugin is not updated?